Matrix versions of Real and Quaternionic Nullstellensätze

Cimprič, Jaka (author)

Real Nullstellensatz is a classical result from Real Algebraic Geometry. It has recently been extended to quaternionic polynomials by Alon and Paran. The aim of this paper is to extend their Quaternionic Nullstellensatz to matrix polynomials. We also obtain an improvement of the Real Nullstellensatz for matrix polynomials in the sense that we simplify the definition of a real left ideal. We use the methods from the proof of the matrix version of Hilbert's Nullstellensatz and we obtain their extensions to a mildly non-commutative case and to the real case.

• Language: English
• Keywords: Real Algebraic Geometry, Nullstellensatz, polynomials over division algebras, matrix rings, quaternions
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2022
• Number of pages: Str. 752-772
• Numbering: Vol. 610
• PID: 20.500.12556/RUL-144094
• UDC: 512.552
• ISSN on article: 0021-8693
• DOI: 10.1016/j.jalgebra.2022.06.038
• COBISS.SI-ID: 139324931
• Publication date in RUL: 31.01.2023

Record is a part of a journal

• Title: Journal of algebra
• Shortened title: J. algebra
• Publisher: Elsevier
• ISSN: 0021-8693
• COBISS.SI-ID: 1310986

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: algebraična geometrija, izreki o ničlah, polinomi nad nekomutativnimi obsegi, matrični kolobarji, kvaternioni

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika